A remarkable collection of Babylonian mathematical texts
A remarkable collection of Babylonian mathematical texts
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巴比伦数学文本的非凡合集
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发表时间：
2007
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通讯作者：
J. Friberg
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作者：
J. Friberg
大约 120 部新的美索不达米亚数学楔形文字文本，全部来自挪威 Schøyen 收藏，在作者的著作《巴比伦数学文本的杰出收藏》（A Remarkable Collection of Babylonian Mathematical Texts）（施普林格，2007 年）中出版。大多数文本是古巴比伦文本（公元前 1900 年至 1600 年），但也有一些文本更古老（苏美尔文本）或更年轻的文本（卡西特文本）。除了对这些新文本的介绍和讨论之外，本书还对美索不达米亚数学的一般重要方面进行了广泛而相当彻底的说明，从公元前 4 世纪末期的开始到公元前 1 世纪末期的最后一次表现。1 本文包含对 Schøyen Collection 中精选的有趣数学楔形文字文本（以 MS 开头的泥板编号）的简要介绍。事实上，Schøyen 收藏中的数学楔形文字文本子集非常广泛，以至于我们可以用其中的例子来详细跟踪古巴比伦抄写学校学生在书写和计算能力方面的进展，从一年级学生用大而笨拙的数字符号写的初级乘法练习，到熟练的模范学生用可靠的手写出的高级数学问题文本，用几乎微观的小楔形文字符号。初学者的带有大数字符号的乘法练习。图 1 显示了一个年轻学生的乘法练习示例，首先以浮点值表示法中的六十进制数计算乘积 50×45 = 37 30。（十进制数的相应结果当然是 50×45 = 2,250 = 37×60+30。）请注意，没有楔形数字零的符号，但有单独的数字符号，从 1 到 9（直立楔形），以及十位，从 10 到 50（斜楔形）。在现代数字符号的音译中（图 1 左侧），十位在右上角写有一个小圆圈。
A bout 120 new Mesopotamian mathematical cuneiform texts, all from the Norwegian Schøyen Collection, are published in the author’s book A Remarkable Collection of Babylonian Mathematical Texts, Springer (2007). Most of the texts are Old Babylonian (1900–1600 BC), but some are older (Sumerian), or younger (Kassite). In addition to the presentation and discussion of these new texts, the book contains a broad and fairly thorough account of important aspects of Mesopotamian mathematics in general, from its beginnings in the late 4th millennium BC till its last manifestations in the late 1st millennium BC.1 The present paper contains brief presentations of a selection of interesting mathematical cuneiform texts in the Schøyen Collection (tablet numbers beginning with MS). Actually, the subcollection of mathematical cuneiform texts in the Schøyen Collection is so extensive that it is possible to use examples from it to follow in detail the progress of Old Babylonian scribe school students in handwriting and computational ability from the first year student’s elementary multiplication exercises written with large and clumsy number signs to the accomplished model student’s advanced mathematical problem texts written in a sure hand and with almost microscopically small cuneiform signs. A beginner’s multiplication exercises with large number signs. Figure 1 shows an example of a young student’s multiplication exercises, beginning with the computation, in terms of sexagesimal numbers in floating place value notation, of the product 50×45 = 37 30. (The corresponding result in decimal numbers is, of course, 50×45 = 2,250 = 37×60+30.) Note that there was no cuneiform number sign for zero, but instead there were separate number signs for the ones, from 1 to 9 (upright wedges), and for the tens, from 10 to 50 (oblique wedges). In the transliteration to modern number signs (to the left in Figure 1) the tens are written with a little circle in the upper right corner.